the zero behavior seems most wrong. Mathematica also returns various things, depending on where you look, that are not zero. I say you are right about atan2(0,0). At the very least we need consistency. Maybe Ginac/Pynac says it's zero? Anyway, this is now ticket 11423.

I don't know that this will help your computation. You may need to try something more sophisticated - like other branch cuts for the arctangent :( What would you like to get from this computation - perhaps in a simpler case that still has atan2(0,0), in principle.